5.4 Selected Answers

5.4ex I

2.
Premise 1 B=A  
Premise 2 ~B  
Assumption 3 what if.... A
1,3 =E 4 then........ B
2 R 5 then........ ~B
3-5 ~I 6 ~A  
3.  
Premise 1 A  
Premise 2 ~A  
Assumption 3 ....what if ~B
1 R 4 ....then... A
2 R 5 ....then... ~A
3-5 ~E 6 B  
4.  
Premise 1 ~~A  
Assumption 2 ....what if ~A
1 R 3 ....then... ~~A
2-3 ~E 4 A  
5.  
Premise 1 (A&B)>(L&S)  
Premise 2 ~L  
Assumption 3 ....what if A&B
1,3 >E 4 ....then... L&S
4 &E 5 ....then... L
2 R 6 ....then... ~L
3-6 ~I 7 ~(A&B)  

 

      5.4 ex II

 

1.  
Premise 1 (AvL)>(T&U)  
Premise 2 ~T  
Assumption 3 ....what if AvL
1,3 >E 4 ....then... T&U
4 &E 5 ....then... T
2 R 6 ....then... ~T
3-6 ~I 7 ~(AvL)  
2.  
Premise 1 ~(~Lv~M)  
Assumption 2 ....what if ~M
2 vI 3 ....then... ~Lv~M
1 R 4 ....then... ~(~Lv~M)
2-4 ~E 5 M  
3.  
Premise 1 ~(A&B)  
Premise 2 A  
Assumption 3 ....what if B
2,3 &I 4 ....then... A&B
1 R 5 ....then... ~(A&B)
3-5 ~I 6 ~B